Isoquant shows different combinations of labour and capital, which can be employed to produce a given level of output. All combinations on one isoquant show the same output, and a higher isoquant indicates higher output.
Isoquant is downward sloping, as more quantity of a factor of production (for example, labour) is required to produce the same output if the firm chooses to hire fewer units of the other input e.g.
capital. The substitution of capital with labour results in a movement along isoquant, as indicated in diagram 5.2.
www.youtube.com/megalecture
www.megalecture.com
Understanding Economics 78 5- Cost Curves in the Long Run
Diagram 5.2
K
L 1Q
An isoquant is not a straight line, rather it is convex if viewed from the origin i.e. its slope decreases throughout. The reason for the convex shape of an isoquant is that the firm is required to give up smaller and smaller quantities of capital (K) to have additional units of labour (L) to produce the same output. This is because of the law of diminishing marginal utility. The following table helps to explain this:
L 1 2 3 4 5 K 20 15 11 8 6
All combinations of K and L shown in this table are on the same isoquant, thus generating the same output. In order to substitute capital for labour i.e. to increase labour quantity from 1 to 2, the firm is required to give up 5 units of capital, as the loss of output by not having 5 units of capital is compensated by having one more unit of labour. However, the marginal product (MP) of the third unit of labour is lesser than the second, so the firm is required to give up a smaller quantity of capital (only 4 K) when it chooses to employ the third unit of labour. Similarly, for the fourth unit of labour, the firm is required to sacrifice an even smaller quantity of capital (3 K). The slope of isoquant is known as Marginal Rate of Factor Substitution (MRS), which decreases throughout, along an isoquant. MRS is the ratio of the change in K to the change in L. It is also the ratio of MPK to MPL. For example, if MPK is 20 units and MPL is 10 units, the firm is required to hire 2 more units of labour to compensate for the loss in output for not having 1 unit of capital, so the slope of isoquant is;
L K
dK MP 20
2K / L dL MP 10
An isocost shows all possible combinations of labour and capital that a firm can employ with given resources and fixed factor i.e. wage rate (w) and interest rate (r). Assuming the firm has 10 and w and r are £2 and £1 per unit respectively, any of the following combinations of L and K can be employed.
L 5 4 3 2 1 0
K 0 2 4 6 8 10
www.youtube.com/megalecture
www.megalecture.com
Understanding Economics 79 5- Cost Curves in the Long Run
Diagram 5.3
10 8 6 4
1 2 3 4 5 L K
O 2
The following equation assumes, that all resources being spent on employing labor and capital.
R = w. L+ r. K Where:
R = Firm‟s money resources
w = wage rate/ hour r = Cost of capital/hour
L = Quantity of Labor employed K = Quantity of capital employed Dividing both sides by r,
R w
. L K
r r
Rearranging,
R w
K . L
r r
This is the linear equation of the isocost whereR
r is the vertical intercept, R
w is the horizontal intercept andw
r , the slope of the isocost. The slope is negative as the isocost is downward sloping. (See diagram 5.4)
Diagram 5.4
L K
R
R w
r
r
w
www.youtube.com/megalecture
www.megalecture.com
Understanding Economics 80 5- Cost Curves in the Long Run
Least Cost Combination of Factors
The least cost combination is given by the intersection of isocost and isoquant as shown in the following diagram.
Diagram 5.5
K
K1
L1 L
D A
B
C E
Though factor combinations A, B and C result in the same output, the firm will choose B, as combinations A and C lie outside isocost, and are hence unaffordable. Similarly, combinations D, B and E lie on the same isocost and hence cost the same to the firm, but the firm chooses B, as combinations D and E are on lower isoquants, giving lesser output to the firm. Thus, the combination B minimizes the cost of producing this output, where the firm employs L1 units of labour and K1 units of capital. The slope of the isoquant is MPL / MPK and the slope of the isocost isw / r, so at the point of intersection, MPL / MPK equals w / r, which is exactly similar to the condition of least cost factor combination established earlier with the help of a numerical example.
Long run average cost curve
The relationship between short and long run average cost curves is shown in diagram 5.6. The long run average cost curve is tangential to SRAC curves.
Diagram 5.6 Costs
MES
LRAC
Q SRAC1
SRAC2 SRAC3 SRAC4
www.youtube.com/megalecture
www.megalecture.com
Understanding Economics 81 5- Cost Curves in the Long Run
Assume that the firm owns one factory whose short run average cost curve is SRAC1. The firm can only increase production by setting up another factory in the long run with SRAC2, which is lower than SRAC1 due to economies of scale. It continues to exploit economies of scale till control and co ordination issues spring up and it reaches a higher average cost curve, SRAC4. Long run average cost curve is also known as the envelope curve, as it touches and envelopes all the short run average cost curves. (Attempt N/03/3/11)